An optimal lower bound in fractional spectral geometry for planar sets with topological constraints
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910337099366400 |
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| author | Bianchi, Francesca Brasco, Lorenzo |
| author_facet | Bianchi, Francesca Brasco, Lorenzo |
| contents | We prove a lower bound on the first eigenvalue of the fractional Dirichlet-Laplacian of order $s$ on planar open sets, in terms of their inradius and topology. The result is optimal, in many respects. In particular, we recover a classical result proved independently by Croke, Osserman and Taylor, in the limit as $s$ goes to $1$. The limit as $s$ goes to $1/2$ is carefully analyzed, as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_08017 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An optimal lower bound in fractional spectral geometry for planar sets with topological constraints Bianchi, Francesca Brasco, Lorenzo Analysis of PDEs Spectral Theory 47A75, 39B72, 35R11 We prove a lower bound on the first eigenvalue of the fractional Dirichlet-Laplacian of order $s$ on planar open sets, in terms of their inradius and topology. The result is optimal, in many respects. In particular, we recover a classical result proved independently by Croke, Osserman and Taylor, in the limit as $s$ goes to $1$. The limit as $s$ goes to $1/2$ is carefully analyzed, as well. |
| title | An optimal lower bound in fractional spectral geometry for planar sets with topological constraints |
| topic | Analysis of PDEs Spectral Theory 47A75, 39B72, 35R11 |
| url | https://arxiv.org/abs/2301.08017 |